Raghu et al. [1]} propose two interrelated effective complexity measures for deep neural networks with piecewise linear activation functions, especially ReLU and hard Tanh [2]}.
Specifically, they define trajectory \(x(t)\)  between two input points \(x_1, x_2 \in \mathbb {R}^d\) , which is a curve parametrized by a scalar \(t \in [0,1]\) , with \(x(0)=x_1\)  and \(x(1)=x_2\) . The first effective complexity measure they propose is the number of linear regions in the input space when sweeping an input point through a trajectory path \(x(t)\) , that is, the effective complexity \(EMC(\mathcal {N})\)  of model \(\mathcal {N}\)  is
\(\nonumber EMC(\mathcal {N}) = \mathcal {T}(\mathcal {N}(x(t); W))\) 
